22. The means of samples of sizes 50 and 75 are 60 and x respectively. If the
mean
of the combined group is 54 ; find x
Answers
Step-by-step explanation:
Given:-
The means of samples of sizes 50 and 75 are 60 and x respectively. And the mean of the combined group is 54 .
To find:-
Find x?
Solution:-
The mean of samples of sizes 50 = 60
The total samples of sizes 50
=> 50×60
=> 3000
The mean of samples of sizes 75 = X
The total samples of sizes 75
=> 75×X
=> 75X
Total number of both samples of both sizes
=> 3000+75X
Total sizes of both samples
= 50+75
= 125
We know that
Mean = Sum of all observations/Number of all observations
=> Mean = (3000+75X)/125
According to the given problem
Mean of the combined group = 54
=> (3000+75X)/125 = 54
=> 3000+75X = 54×125
=> 3000+75X = 6750
=>75X = 6750-3000
=> 75X = 3750
=> X = 3750/75
=> X = 50
Alternative Method:-
Combined Mean = (f1x1+f1x2+...+fnxn)/(f1+f2+...+fn)
=> [(50×60)+(75×X)]/(50+75) = 54
=> (3000+75X)/125 = 54
=>3000+75X = 54×125
=> 3000+75X = 6750
=> 75X = 6750-3000
=>75X = 3750
=>X = 3750/75
=> X = 50
Answer:-
The value of X for the given problem is 50
Used formulae:-
- Mean = Sum of all observations/Number of all observations